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SS.py
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SS.py
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# imports
from re import VERBOSE
import numpy as np
import scipy.optimize as opt
from dask import delayed, compute
import dask.multiprocessing
from ogcore import tax, household, firm, utils, fiscal
from ogcore import aggregates as aggr
from ogcore.constants import SHOW_RUNTIME
import os
import warnings
if not SHOW_RUNTIME:
warnings.simplefilter("ignore", RuntimeWarning)
"""
Set minimizer tolerance
"""
MINIMIZER_TOL = 1e-13
"""
Set flag for enforcement of solution check
"""
ENFORCE_SOLUTION_CHECKS = True
"""
Set flag for verbosity
"""
VERBOSE = True
"""
A global future for the Parameters object for client workers.
This is scattered once and place at module scope, then used
by the client in the inner loop.
"""
scattered_p = None
"""
------------------------------------------------------------------------
Define Functions
------------------------------------------------------------------------
"""
def euler_equation_solver(guesses, *args):
"""
Finds the euler errors for certain b and n, one ability type at a
time.
Args:
guesses (Numpy array): initial guesses for b and n, length 2S
args (tuple): tuple of arguments (r, w, p_tilde, bq, TR, factor, j, p)
r (scalar): real interest rate
w (scalar): real wage rate
p_tilde (scalar): composite good price
bq (Numpy array): bequest amounts by age, length S
tr (scalar): government transfer amount by age, length S
ubi (vector): universal basic income (UBI) payment, length S
factor (scalar): scaling factor converting model units to dollars
p (OG-Core Specifications object): model parameters
Returns:
errros (Numpy array): errors from FOCs, length 2S
"""
(r, w, p_tilde, bq, tr, ubi, factor, j, p) = args
b_guess = np.array(guesses[: p.S])
n_guess = np.array(guesses[p.S :])
b_s = np.array([0] + list(b_guess[:-1]))
b_splus1 = b_guess
theta = tax.replacement_rate_vals(n_guess, w, factor, j, p)
error1 = household.FOC_savings(
r,
w,
p_tilde,
b_s,
b_splus1,
n_guess,
bq,
factor,
tr,
ubi,
theta,
p.rho[-1, :],
p.etr_params[-1],
p.mtry_params[-1],
None,
j,
p,
"SS",
)
error2 = household.FOC_labor(
r,
w,
p_tilde,
b_s,
b_splus1,
n_guess,
bq,
factor,
tr,
ubi,
theta,
p.chi_n[-1, :],
p.etr_params[-1],
p.mtrx_params[-1],
None,
j,
p,
"SS",
)
# Put in constraints for consumption and savings.
# According to the euler equations, they can be negative. When
# Chi_b is large, they will be. This prevents that from happening.
# I'm not sure if the constraints are needed for labor.
# But we might as well put them in for now.
mask1 = n_guess < 0
mask2 = n_guess > p.ltilde
mask3 = b_guess <= 0
mask4 = np.isnan(n_guess)
mask5 = np.isnan(b_guess)
error2[mask1] = 1e14
error2[mask2] = 1e14
error1[mask3] = 1e14
error1[mask5] = 1e14
error2[mask4] = 1e14
taxes = tax.net_taxes(
r,
w,
b_s,
n_guess,
bq,
factor,
tr,
ubi,
theta,
None,
j,
False,
"SS",
p.e[-1, :, j],
p.etr_params[-1],
p,
)
cons = household.get_cons(
r,
w,
p_tilde,
b_s,
b_splus1,
n_guess,
bq,
taxes,
p.e[-1, :, j],
p,
)
mask6 = cons < 0
error1[mask6] = 1e14
errors = np.hstack((error1, error2))
return errors
def inner_loop(outer_loop_vars, p, client):
"""
This function solves for the inner loop of the SS. That is, given
the guesses of the outer loop variables (r, w, TR, factor) this
function solves the households' problems in the SS.
Args:
outer_loop_vars (tuple): tuple of outer loop variables,
(bssmat, nssmat, r_p, r, w, p_m, BQ, TR, factor) or
(bssmat, nssmat, r_p, r, w, p_m, BQ, Y, TR, factor)
bssmat (Numpy array): initial guess at savings, size = SxJ
nssmat (Numpy array): initial guess at labor supply, size = SxJ
r_p (scalar): return on household investment portfolio
r (scalar): real interest rate
w (scalar): real wage rate
p_m (array_like): production goods prices
BQ (array_like): aggregate bequest amount(s)
TR (scalar): lump sum transfer amount
Y (scalar): real GDP
factor (scalar): scaling factor converting model units to dollars
p (OG-Core Specifications object): model parameters
client (Dask client object): client
Returns:
(tuple): results from household solution:
* euler_errors (Numpy array): errors terms from FOCs,
size = 2SxJ
* bssmat (Numpy array): savings, size = SxJ
* nssmat (Numpy array): labor supply, size = SxJ
* new_r (scalar): real interest rate on firm capital
* new_r_gov (scalar): real interest rate on government debt
* new_r_p (scalar): real interest rate on household
portfolio
* new_w (scalar): real wage rate
* new_p_i (array_like): good prices
* K_vec (array_like): capital demand for each industry
* L_vec (array_like): labor demand for each industry
* Y_vec (array_like): output from each industry
* new_TR (scalar): lump sum transfer amount
* new_Y (scalar): real GDP
* new_factor (scalar): scaling factor converting model
units to dollars
* new_BQ (array_like): aggregate bequest amount(s)
* average_income_model (scalar): average income in model
units
"""
# Retrieve the "scattered" Parameters object.
global scattered_p
if scattered_p is None:
scattered_p = client.scatter(p, broadcast=True) if client else p
# unpack variables to pass to function
bssmat, nssmat, r_p, r, w, p_m, Y, BQ, TR, factor = outer_loop_vars
p_m = np.array(p_m) # TODO: why is this a list otherwise?
p_i = np.dot(p.io_matrix, p_m)
BQ = np.array(BQ)
# initialize array for euler errors
euler_errors = np.zeros((2 * p.S, p.J))
p_tilde = aggr.get_ptilde(p_i, p.tau_c[-1, :], p.alpha_c)
bq = household.get_bq(BQ, None, p, "SS")
tr = household.get_tr(TR, None, p, "SS")
ubi = p.ubi_nom_array[-1, :, :] / factor
lazy_values = []
for j in range(p.J):
guesses = np.append(bssmat[:, j], nssmat[:, j])
euler_params = (
r_p,
w,
p_tilde,
bq[:, j],
tr[:, j],
ubi[:, j],
factor,
j,
scattered_p,
)
lazy_values.append(
delayed(opt.root)(
euler_equation_solver,
guesses * 0.9,
args=euler_params,
method=p.FOC_root_method,
tol=MINIMIZER_TOL,
)
)
if client:
futures = client.compute(lazy_values, num_workers=p.num_workers)
results = client.gather(futures)
else:
results = results = compute(
*lazy_values,
scheduler=dask.multiprocessing.get,
num_workers=p.num_workers,
)
for j, result in enumerate(results):
euler_errors[:, j] = result.fun
bssmat[:, j] = result.x[: p.S]
nssmat[:, j] = result.x[p.S :]
b_splus1 = bssmat
b_s = np.array(list(np.zeros(p.J).reshape(1, p.J)) + list(bssmat[:-1, :]))
theta = tax.replacement_rate_vals(nssmat, w, factor, None, p)
num_params = len(p.etr_params[-1][0])
etr_params_3D = [
[
[p.etr_params[-1][s][i] for i in range(num_params)]
for j in range(p.J)
]
for s in range(p.S)
]
net_tax = tax.net_taxes(
r_p,
w,
b_s,
nssmat,
bq,
factor,
tr,
ubi,
theta,
None,
None,
False,
"SS",
np.squeeze(p.e[-1, :, :]),
etr_params_3D,
p,
)
c_s = household.get_cons(
r_p,
w,
p_tilde,
b_s,
b_splus1,
nssmat,
bq,
net_tax,
np.squeeze(p.e[-1, :, :]),
p,
)
c_i = household.get_ci(c_s, p_i, p_tilde, p.tau_c[-1, :], p.alpha_c)
L = aggr.get_L(nssmat, p, "SS")
B = aggr.get_B(bssmat, p, "SS", False)
# Find gov't debt
r_gov = fiscal.get_r_gov(r, p, "SS")
D, D_d, D_f, new_borrowing, _, new_borrowing_f = fiscal.get_D_ss(
r_gov, Y, p
)
I_g = fiscal.get_I_g(Y, p.alpha_I[-1])
K_g = fiscal.get_K_g(0, I_g, p, "SS")
# Find wage rate consistent with open economy interest rate
# this is an approximation - assumes only KL in rest of world
# production function
w_open = firm.get_w_from_r(p.world_int_rate[-1], p, "SS")
# Find output, labor demand, capital demand for M-1 industries
L_vec = np.zeros(p.M)
K_vec = np.zeros(p.M)
C_vec = np.zeros(p.I)
K_demand_open_vec = np.zeros(p.M)
for i_ind in range(p.I):
C_vec[i_ind] = aggr.get_C(c_i[i_ind, :, :], p, "SS")
Y_vec = np.dot(p.io_matrix.T, C_vec)
for m_ind in range(p.M - 1):
KYrat_m = firm.get_KY_ratio(r, p_m, p, "SS", m_ind)
K_vec[m_ind] = KYrat_m * Y_vec[m_ind]
L_vec[m_ind] = firm.solve_L(
Y_vec[m_ind], K_vec[m_ind], K_g, p, "SS", m_ind
)
K_demand_open_vec[m_ind] = firm.get_K(
p.world_int_rate[-1], w_open, L_vec[m_ind], p, "SS", m_ind
)
# Find output, labor demand, capital demand for industry M
L_M = max(0.001, L - L_vec.sum()) # make sure L_M > 0
K_demand_open_vec[-1] = firm.get_K(
p.world_int_rate[-1], w_open, L_M, p, "SS", -1
)
K, K_d, K_f = aggr.get_K_splits(
B, K_demand_open_vec.sum(), D_d, p.zeta_K[-1]
)
K_M = max(0.001, K - K_vec.sum()) # make sure K_M > 0
L_vec[-1] = L_M
K_vec[-1] = K_M
Y_vec[-1] = firm.get_Y(K_vec[-1], K_g, L_vec[-1], p, "SS", -1)
# Find GDP
Y = (p_m * Y_vec).sum()
I_g = fiscal.get_I_g(Y, p.alpha_I[-1])
K_g = fiscal.get_K_g(0, I_g, p, "SS")
if p.zeta_K[-1] == 1.0:
new_r = p.world_int_rate[-1]
else:
new_r = firm.get_r(Y_vec[-1], K_vec[-1], p_m, p, "SS", -1)
new_w = firm.get_w(Y_vec[-1], L_vec[-1], p_m, p, "SS")
new_r_gov = fiscal.get_r_gov(new_r, p, "SS")
# now get accurate measure of debt service cost
(
D,
D_d,
D_f,
new_borrowing,
debt_service,
new_borrowing_f,
) = fiscal.get_D_ss(new_r_gov, Y, p)
MPKg_vec = np.zeros(p.M)
for m in range(p.M):
MPKg_vec[m] = firm.get_MPx(Y_vec[m], K_g, p.gamma_g[m], p, "SS", m)
new_r_p = aggr.get_r_p(
new_r, new_r_gov, p_m, K_vec, K_g, D, MPKg_vec, p, "SS"
)
average_income_model = (
(new_r_p * b_s + new_w * np.squeeze(p.e[-1, :, :]) * nssmat)
* p.omega_SS.reshape(p.S, 1)
* p.lambdas.reshape(1, p.J)
).sum()
if p.baseline:
new_factor = p.mean_income_data / average_income_model
else:
new_factor = factor
new_BQ = aggr.get_BQ(new_r_p, bssmat, None, p, "SS", False)
new_bq = household.get_bq(new_BQ, None, p, "SS")
tr = household.get_tr(TR, None, p, "SS")
theta = tax.replacement_rate_vals(nssmat, new_w, new_factor, None, p)
# Find updated goods prices
new_p_m = firm.get_pm(new_w, Y_vec, L_vec, p, "SS")
new_p_m = new_p_m / new_p_m[-1] # normalize prices by industry M
new_p_i = np.dot(p.io_matrix, new_p_m)
new_p_tilde = aggr.get_ptilde(new_p_i, p.tau_c[-1, :], p.alpha_c)
num_params = len(p.etr_params[-1][0])
etr_params_3D = [
[
[p.etr_params[-1][s][i] for i in range(num_params)]
for j in range(p.J)
]
for s in range(p.S)
]
taxss = tax.net_taxes(
new_r_p,
new_w,
b_s,
nssmat,
new_bq,
factor,
tr,
ubi,
theta,
None,
None,
False,
"SS",
np.squeeze(p.e[-1, :, :]),
etr_params_3D,
p,
)
cssmat = household.get_cons(
new_r_p,
new_w,
new_p_tilde,
b_s,
bssmat,
nssmat,
new_bq,
taxss,
np.squeeze(p.e[-1, :, :]),
p,
)
(
total_tax_revenue,
_,
agg_pension_outlays,
UBI_outlays,
_,
_,
_,
_,
_,
_,
) = aggr.revenue(
new_r_p,
new_w,
b_s,
nssmat,
new_bq,
c_i,
Y_vec,
L_vec,
K_vec,
new_p_m,
factor,
ubi,
theta,
etr_params_3D,
np.squeeze(p.e[-1, :, :]),
p,
None,
"SS",
)
G = fiscal.get_G_ss(
Y,
total_tax_revenue,
agg_pension_outlays,
TR,
UBI_outlays,
I_g,
new_borrowing,
debt_service,
p,
)
new_TR = fiscal.get_TR(
Y,
TR,
G,
total_tax_revenue,
agg_pension_outlays,
UBI_outlays,
I_g,
p,
"SS",
)
G_vec = np.zeros(p.M)
G_vec[-1] = G
C_m_vec = np.dot(p.io_matrix.T, C_vec)
I_d_vec = np.zeros(p.M)
I_d = aggr.get_I(b_splus1, K_d, K_d, p, "SS")
I_d_vec[-1] = I_d
I_g_vec = np.zeros(p.M)
I_g_vec[-1] = I_g
debt_service_f = fiscal.get_debt_service_f(r_p, D_f)
net_capital_outflows = aggr.get_capital_outflows(
r_p, K_f, new_borrowing_f, debt_service_f, p
)
net_capital_outflows_vec = np.zeros(p.M)
net_capital_outflows_vec[-1] = net_capital_outflows
rc_error = (
Y_vec - C_m_vec - G_vec - I_d_vec - I_g_vec - net_capital_outflows_vec
)
return (
euler_errors,
bssmat,
nssmat,
new_r,
new_r_gov,
new_r_p,
new_w,
new_p_m,
K_vec,
L_vec,
Y_vec,
new_TR,
Y,
new_factor,
new_BQ,
average_income_model,
)
def SS_solver(
bmat, nmat, r_p, r, w, p_m, Y, BQ, TR, factor, p, client, fsolve_flag=False
):
"""
Solves for the steady state distribution of capital, labor, as well
as w, r, TR and the scaling factor, using functional iteration.
Args:
bmat (Numpy array): initial guess at savings, size = SxJ
nmat (Numpy array): initial guess at labor supply, size = SxJ
r_p (scalar): return on household investment portfolio
r (scalar): real interest rate
w (scalar): real wage rate
p_m (array_like): good prices
Y (scalar): real GDP
BQ (array_like): aggregate bequest amount(s)
TR (scalar): lump sum transfer amount
factor (scalar): scaling factor converting model units to dollars
p (OG-Core Specifications object): model parameters
client (Dask client object): client
Returns:
output (dictionary): dictionary with steady state solution
results
"""
dist = 10
iteration = 0
dist_vec = np.zeros(p.maxiter)
maxiter_ss = p.maxiter
nu_ss = p.nu
if fsolve_flag: # case where already solved via SS_fsolve
maxiter_ss = 1
if p.baseline_spending:
TR_ss = TR
if not p.budget_balance and not p.baseline_spending:
Y = TR / p.alpha_T[-1]
while (dist > p.mindist_SS) and (iteration < maxiter_ss):
# Solve for the steady state levels of b and n, given w, r,
# Y, BQ, TR, and factor
if p.baseline_spending:
TR = TR_ss
if not p.budget_balance and not p.baseline_spending:
Y = TR / p.alpha_T[-1]
outer_loop_vars = (bmat, nmat, r_p, r, w, p_m, Y, BQ, TR, factor)
(
euler_errors,
new_bmat,
new_nmat,
new_r,
new_r_gov,
new_r_p,
new_w,
new_p_m,
new_K_vec,
new_L_vec,
new_Y_vec,
new_TR,
new_Y,
new_factor,
new_BQ,
average_income_model,
) = inner_loop(outer_loop_vars, p, client)
# update guesses for next iteration
bmat = utils.convex_combo(new_bmat, bmat, nu_ss)
nmat = utils.convex_combo(new_nmat, nmat, nu_ss)
r_p = utils.convex_combo(new_r_p, r_p, nu_ss)
r = utils.convex_combo(new_r, r, nu_ss)
w = utils.convex_combo(new_w, w, nu_ss)
p_m = utils.convex_combo(new_p_m, p_m, nu_ss)
factor = utils.convex_combo(new_factor, factor, nu_ss)
BQ = utils.convex_combo(new_BQ, BQ, nu_ss)
if p.baseline_spending:
Y = utils.convex_combo(new_Y, Y, nu_ss)
if Y != 0:
dist = np.array(
[utils.pct_diff_func(new_r, r)]
+ [utils.pct_diff_func(new_r_p, r_p)]
+ [utils.pct_diff_func(new_w, w)]
+ list(utils.pct_diff_func(new_p_m, p_m))
+ list(utils.pct_diff_func(new_BQ, BQ))
+ [utils.pct_diff_func(new_Y, Y)]
+ [utils.pct_diff_func(new_factor, factor)]
).max()
else:
# If Y is zero (if there is no output), a percent difference
# will throw NaN's, so we use an absolute difference
dist = np.array(
[utils.pct_diff_func(new_r, r)]
+ [utils.pct_diff_func(new_r_p, r_p)]
+ [utils.pct_diff_func(new_w, w)]
+ list(utils.pct_diff_func(new_p_m, p_m))
+ list(utils.pct_diff_func(new_BQ, BQ))
+ [abs(new_Y - Y)]
+ [utils.pct_diff_func(new_factor, factor)]
).max()
else:
if p.baseline_spending:
TR = TR_ss
else:
TR = utils.convex_combo(new_TR, TR, nu_ss)
dist = np.array(
[float(utils.pct_diff_func(new_r, r))]
+ [float(utils.pct_diff_func(new_r_p, r_p))]
+ [float(utils.pct_diff_func(new_w, w))]
+ list(utils.pct_diff_func(new_p_m, p_m))
+ list(utils.pct_diff_func(new_BQ, BQ))
+ [float(utils.pct_diff_func(new_TR, TR))]
+ [float(utils.pct_diff_func(new_factor, factor))]
).max()
dist_vec[iteration] = dist
# Similar to TPI: if the distance between iterations increases, then
# decrease the value of nu to prevent cycling
if iteration > 10:
if dist_vec[iteration] - dist_vec[iteration - 1] > 0:
nu_ss /= 2.0
print("New value of nu:", nu_ss)
iteration += 1
if VERBOSE:
print("Iteration: %02d" % iteration, " Distance: ", dist)
# Generate the SS values of variables, including euler errors
bssmat_s = np.append(np.zeros((1, p.J)), bmat[:-1, :], axis=0)
bssmat_splus1 = bmat
nssmat = nmat
rss = new_r
wss = new_w
K_vec_ss = new_K_vec
L_vec_ss = new_L_vec
Y_vec_ss = new_Y_vec
r_gov_ss = fiscal.get_r_gov(rss, p, "SS")
p_m_ss = new_p_m
p_i_ss = np.dot(p.io_matrix, p_m_ss)
p_tilde_ss = aggr.get_ptilde(p_i_ss, p.tau_c[-1, :], p.alpha_c)
TR_ss = new_TR
Yss = new_Y
I_g_ss = fiscal.get_I_g(Yss, p.alpha_I[-1])
K_g_ss = fiscal.get_K_g(0, I_g_ss, p, "SS")
Lss = aggr.get_L(nssmat, p, "SS")
Bss = aggr.get_B(bssmat_splus1, p, "SS", False)
(
Dss,
D_d_ss,
D_f_ss,
new_borrowing,
debt_service,
new_borrowing_f,
) = fiscal.get_D_ss(r_gov_ss, Yss, p)
print("SS debt = ", Dss, new_borrowing_f)
w_open = firm.get_w_from_r(p.world_int_rate[-1], p, "SS")
K_demand_open_ss = np.zeros(p.M)
for m in range(p.M):
K_demand_open_ss[m] = firm.get_K(
p.world_int_rate[-1], w_open, L_vec_ss[m], p, "SS", m
)
Kss, K_d_ss, K_f_ss = aggr.get_K_splits(
Bss, K_demand_open_ss.sum(), D_d_ss, p.zeta_K[-1]
)
# Yss = firm.get_Y(Kss, K_g_ss, Lss, p, 'SS')
I_g_ss = fiscal.get_I_g(Yss, p.alpha_I[-1])
K_g_ss = fiscal.get_K_g(0, I_g_ss, p, "SS")
MPKg_vec = np.zeros(p.M)
for m in range(p.M):
MPKg_vec[m] = firm.get_MPx(
Y_vec_ss[m], K_g_ss, p.gamma_g[m], p, "SS", m
)
# r_p_ss = aggr.get_r_p(
# rss, r_gov_ss, p_m_ss, K_vec_ss, K_g_ss, Dss, MPKg_vec, p, "SS"
# )
r_p_ss = new_r_p
# Note that implicitly in this computation is that immigrants'
# wealth is all in the form of private capital
I_d_ss = aggr.get_I(bssmat_splus1, K_d_ss, K_d_ss, p, "SS")
Iss = aggr.get_I(bssmat_splus1, Kss, Kss, p, "SS")
BQss = new_BQ
factor_ss = factor
bqssmat = household.get_bq(BQss, None, p, "SS")
trssmat = household.get_tr(TR_ss, None, p, "SS")
ubissmat = p.ubi_nom_array[-1, :, :] / factor_ss
theta = tax.replacement_rate_vals(nssmat, wss, factor_ss, None, p)
# Compute effective and marginal tax rates for all agents
num_params = len(p.etr_params[-1][0])
etr_params_3D = [
[
[p.etr_params[-1][s][i] for i in range(num_params)]
for j in range(p.J)
]
for s in range(p.S)
]
mtrx_params_3D = [
[
[p.mtrx_params[-1][s][i] for i in range(num_params)]
for j in range(p.J)
]
for s in range(p.S)
]
mtry_params_3D = [
[
[p.mtry_params[-1][s][i] for i in range(num_params)]
for j in range(p.J)
]
for s in range(p.S)
]
labor_noncompliance_rate_2D = np.tile(
np.reshape(p.labor_income_tax_noncompliance_rate[-1, :], (1, p.J)),
(p.S, 1),
)
capital_noncompliance_rate_2D = np.tile(
np.reshape(p.labor_income_tax_noncompliance_rate[-1, :], (1, p.J)),
(p.S, 1),
)
mtry_ss = tax.MTR_income(
r_p_ss,
wss,
bssmat_s,
nssmat,
factor,
True,
np.squeeze(p.e[-1, :, :]),
etr_params_3D,
mtry_params_3D,
capital_noncompliance_rate_2D,
p,
)
mtrx_ss = tax.MTR_income(
r_p_ss,
wss,
bssmat_s,
nssmat,
factor,
False,
np.squeeze(p.e[-1, :, :]),
etr_params_3D,
mtrx_params_3D,
labor_noncompliance_rate_2D,
p,
)
etr_ss = tax.ETR_income(
r_p_ss,
wss,
bssmat_s,
nssmat,
factor,
np.squeeze(p.e[-1, :, :]),
etr_params_3D,
labor_noncompliance_rate_2D,
capital_noncompliance_rate_2D,
p,
)
taxss = tax.net_taxes(
r_p_ss,
wss,
bssmat_s,
nssmat,
bqssmat,
factor_ss,
trssmat,
ubissmat,
theta,
None,
None,
False,
"SS",
np.squeeze(p.e[-1, :, :]),
etr_params_3D,
p,
)
cssmat = household.get_cons(
r_p_ss,
wss,
p_tilde_ss,
bssmat_s,
bssmat_splus1,
nssmat,
bqssmat,
taxss,
np.squeeze(p.e[-1, :, :]),
p,
)
yss_before_tax_mat = household.get_y(
r_p_ss, wss, bssmat_s, nssmat, p, "SS"
)
Css = aggr.get_C(cssmat, p, "SS")
c_i_ss_mat = household.get_ci(
cssmat, p_i_ss, p_tilde_ss, p.tau_c[-1, :], p.alpha_c
)
C_vec_ss = np.zeros(p.I)
for i_ind in range(
p.I
): # TODO: update aggr.get_C to take full IxSxJ array
C_vec_ss[i_ind] = aggr.get_C(
c_i_ss_mat[i_ind, :, :],
p,
"SS",
)
(
total_tax_revenue,
iit_payroll_tax_revenue,
agg_pension_outlays,
UBI_outlays,
bequest_tax_revenue,
wealth_tax_revenue,
cons_tax_revenue,
business_tax_revenue,
payroll_tax_revenue,
iit_revenue,
) = aggr.revenue(
r_p_ss,
wss,
bssmat_s,
nssmat,
bqssmat,
c_i_ss_mat,
Y_vec_ss,
L_vec_ss,
K_vec_ss,
p_m,
factor,
ubissmat,
theta,
etr_params_3D,
np.squeeze(p.e[-1, :, :]),
p,
None,
"SS",
)
Gss = fiscal.get_G_ss(
Yss,
total_tax_revenue,
agg_pension_outlays,
TR_ss,
UBI_outlays,
I_g_ss,
new_borrowing,
debt_service,
p,
)
# Compute total investment (not just domestic)
Iss_total = aggr.get_I(None, Kss, Kss, p, "total_ss")
# solve resource constraint
# net foreign borrowing
debt_service_f = fiscal.get_debt_service_f(r_p_ss, D_f_ss)
net_capital_outflows = aggr.get_capital_outflows(
r_p_ss, K_f_ss, new_borrowing_f, debt_service_f, p
)
# Fill in arrays, noting that M-1 industries only produce consumption goods
G_vec_ss = np.zeros(p.M)
# Map consumption goods back to demands for production goods
print("IO: ", p.io_matrix.T.shape, ", C: ", C_vec_ss.shape)
C_m_vec_ss = np.dot(p.io_matrix.T, C_vec_ss)
G_vec_ss[-1] = Gss
I_d_vec_ss = np.zeros(p.M)
I_d_vec_ss[-1] = I_d_ss
I_g_vec_ss = np.zeros(p.M)
I_g_vec_ss[-1] = I_g_ss
net_capital_outflows_vec = np.zeros(p.M)
net_capital_outflows_vec[-1] = net_capital_outflows
RC = aggr.resource_constraint(
Y_vec_ss,
C_m_vec_ss,
G_vec_ss,
I_d_vec_ss,
I_g_vec_ss,
net_capital_outflows_vec,
)
if VERBOSE:
print("Foreign debt holdings = ", D_f_ss)
print("Foreign capital holdings = ", K_f_ss)
print("resource constraint: ", RC)
if Gss < 0:
print(
"Steady state government spending is negative to satisfy"
+ " budget"
)
if ENFORCE_SOLUTION_CHECKS and (max(np.absolute(RC)) > p.RC_SS):
print("Resource Constraint Difference:", RC)
err = "Steady state aggregate resource constraint not satisfied"
raise RuntimeError(err)
# check constraints
household.constraint_checker_SS(bssmat_splus1, nssmat, cssmat, p.ltilde)
euler_savings = euler_errors[: p.S, :]
euler_labor_leisure = euler_errors[p.S :, :]
if VERBOSE:
print(
"Maximum error in labor FOC = ",
np.absolute(euler_labor_leisure).max(),
)
print(
"Maximum error in savings FOC = ", np.absolute(euler_savings).max()
)
# Return dictionary of SS results
output = {
"Kss": Kss,
"K_f_ss": K_f_ss,
"K_d_ss": K_d_ss,
"K_g_ss": K_g_ss,
"I_g_ss": I_g_ss,
"Bss": Bss,
"Lss": Lss,
"Css": Css,
"Iss": Iss,
"K_vec_ss": K_vec_ss,
"L_vec_ss": L_vec_ss,
"C_vec_ss": C_vec_ss,
"Y_vec_ss": Y_vec_ss,
"Iss_total": Iss_total,
"I_d_ss": I_d_ss,
"nssmat": nssmat,
"Yss": Yss,
"Dss": Dss,
"D_f_ss": D_f_ss,
"D_d_ss": D_d_ss,
"wss": wss,
"rss": rss,
"p_m_ss": p_m_ss,
"total_taxes_ss": taxss,
"ubissmat": ubissmat,
"p_m_ss": p_m_ss,
"p_tilde_ss": p_tilde_ss,
"r_gov_ss": r_gov_ss,
"r_p_ss": r_p_ss,
"theta": theta,
"BQss": BQss,
"factor_ss": factor_ss,
"bssmat_s": bssmat_s,
"cssmat": cssmat,
"bssmat_splus1": bssmat_splus1,
"yss_before_tax_mat": yss_before_tax_mat,
"bqssmat": bqssmat,
"TR_ss": TR_ss,
"trssmat": trssmat,
"Gss": Gss,
"total_tax_revenue": total_tax_revenue,
"business_tax_revenue": business_tax_revenue,
"iit_payroll_tax_revenue": iit_payroll_tax_revenue,
"iit_revenue": iit_revenue,
"payroll_tax_revenue": payroll_tax_revenue,
"agg_pension_outlays": agg_pension_outlays,
"UBI_outlays_SS": UBI_outlays,
"bequest_tax_revenue": bequest_tax_revenue,
"wealth_tax_revenue": wealth_tax_revenue,
"cons_tax_revenue": cons_tax_revenue,